To find: The value of x.

Tammy Todd 2021-08-11 Answered
To find: The value of x.
Given:
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Expert Answer

nitruraviX
Answered 2021-08-12 Author has 16520 answers
In \(\displaystyle\triangle{S}{T}{R},\triangle{V}{W}{U}\):
\(\displaystyle\angle{S}\stackrel{\sim}{=}\angle{V}\)
\(\displaystyle\angle{T}\stackrel{\sim}{=}\angle{W}\)
By A-A similarity, the \(\displaystyle\triangle{S}{T}{R}\sim\triangle{V}{W}{U}\).
SP=PR=x
\(\displaystyle\Rightarrow{S}{R}={2}{x}\)
UQ=QV=3
\(\displaystyle\Rightarrow{U}{V}={6}\)
In two similar triangles, the ratio of their corresponding sides, medians are equal.
\(\displaystyle{\frac{{{S}{R}}}{{{V}{U}}}}={\frac{{{T}{P}}}{{{W}{Q}}}}\)
\(\displaystyle\Rightarrow{\frac{{{2}{x}}}{{{6}}}}={\frac{{{13.5}}}{{{9}}}}\)
\(\displaystyle\Rightarrow{x}={4.5}\)
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